Sustained flight at hypersonic speeds presents an enduring challenge to vehicle design and control. An extreme aerothermal environment acting on geometrically thin, multifunctional structures can result in the significant structural response of key aerodynamic surfaces. Specifically, the oscillations of a compression corner shock-wave/boundary-layer interaction, which models a control surface deflection, can couple with the lowest natural frequencies of a proximal compliant surface, leading to a range of undesirable outcomes from reduced service life to structural failure. The present work investigates these phenomena through time-accurate high-fidelity aeroelastic simulations of a laminar two-dimensional flow at over a 35 deg compression ramp featuring an embedded compliant panel. Surface pressure, skin friction, and heat transfer associated with the corner shock-wave/boundary-layer interaction are directly compared between rigid and compliant configurations. The upstream separation zone is observed to synchronize with the compliant-panel deflection. A reduction in surface heat flux is observed for a majority of compliant cases relative to the rigid case, whereas entirely new flow features are observed in response to large-scale panel deflections. A modification is proposed to the local piston-theory aerodynamic model to improve the accuracy of surface pressure predictions.